I would say that the oldest physics (although it is often seen as "mathematics") is probably the empirical discovery of certain geometrical relationships, which are nothing else but properties of space (before this was cast in a more comprehensive whole by Euclid).

According to "A History of Mechanics" by Dugas, the first recorded textbook devoted to mechanics (simple machines) orginates with Aristotle (384-322 BC), "or, more accurately, with the author of the probably acrocryphal treatise called 'Problems of Mechanics'. Aristotle wrote other texts as well, including 'Physics' and 'Treatise on the Heavens'.

Archimedes (287-212 BC) made statics an autonomous theoretical science with his treatise on the lever.